Statistical modelling and applications using Weibull and Burr III distributions

Abstract

Lifetime data analysis is crucial in areas like reliability engineering, survival analysis, and related fields, as it is essential to accurately model time-to-event data for effective risk assessment, reliability evaluation, and informed decision making. However, classical lifetime distributions often struggle with real-world data complexities such as skewness, heavy tails, and diverse hazard rate be- haviours. To address these challenges, this thesis focuses on the Weibull and Burr III distributions, known for their flexibility and wide applicability, and de- velops new models, regression frameworks, and inferential methods to advance lifetime data analysis. The thesis, titled Statistical Modelling and Applications Using Weibull and Burr III Distributions, is organized into ten chapters. Chapter 1 establishes the theoretical background, covering quantile functions, regression models, censor- ing schemes, and competing risks, alongside a comprehensive literature review. Chapter 2 proposes a new family of distributions combining the quantile func- tions of Burr III and Weibull, examining their key characteristics and reliabil- ity properties. Model parameters are estimated using method of Least Squares and method of L - moments, with performance illustrated through two real-life datasets. Chapter 3 proposes the Burr III Weibull (BIIIW) distribution, ana- lyzes its statistical properties, and develops estimation procedures via maximum likelihood. Its performance is validated through simulations and application to Covid-19 data. Chapter 4 explores the survival features of the Odd Burr III Weibull (OBIIIW) distribution through a comparative analysis between artifi- cial neural networks (ANNs) and the maximum likelihood estimation (MLE) method, showing the promise of ANNs for clinical data modelling. Chapter 5 develops a parametric regression model using OBIIIW to anal- yse censored data and complex hazard patterns such as bathtub-shaped failure rates. Estimation is performed using MLE and jackknife methods, with robust- ness checks via simulations and diagnostics based on influence measures. Chap- ter 6 investigates stress-strength reliability (SSR) when variables follow Weibull Burr III distributions, using maximum likelihood and Bayesian approaches. The performance of the estimators is validated through a simulation study and two real-life clinical datasets. Chapter 7 addresses competing risks under generalized type-II hybrid censoring, employing MLE and Bayesian methods for both point and interval estimation, supported by simulation and real-world applications. Chapter 8 extends SSR analysis to multicomponent systems with non-identical strength components under progressive first failure censoring, applying both clas- sical and Bayesian approaches, and illustrates the practical utility with real data. Chapter 9 summarizes the thesis by highlighting new statistical models, a novel regression model, ANN-based survival analysis, and inferential work on SSR, multicomponent SSR, and competing risk scenarios under censoring frame- work. Chapter 10 outlines future research directions for extending these methods to more complex data and wider applications.